人大陈卫教授手把手教你统计15-MCA.ppt
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人大陈卫教授手把手教你统计15-MCA.ppt
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1,Lecture13MultipleClassificationAnalysis(MCA),2,ThisLectureCovers,TheMCAastheequivalentofamultipleregressionanalysisMCAadaptedtologisticregression,3,Multipleclassificationanalysis(MCA)isusedtoexaminetheeffectofeachindependentvariableonthedependentvariablewhilecontrollingfortheeffectsoftheotherindependentvariables,whenthedependentvariableisanquantitativevariableandtheindependentvariablesarecategorical.,4,MCAismosteasilyexplainedasmultipleregressionwithdummyvariables.Thus,thedependentvariableisaquantitativevariable,andtheindependentvariablesarecategoricalvariables,representedbydummyvariables.,5,MCAwithonecategoricalpredictorvariableisequivalenttoone-wayanalysisofvariance;MCAwithtwocategoricalpredictorvariablesisequivalenttotwo-wayanalysisofvariance;andsoon.,6,ControlvariablesmaybeaddedtotheMCAmodel.Whenquantitativevariables,inadditiontocategoricalvariables,areincludedamongthepredictorvariables,MCAisequivalenttowhatiscommonlycalledanalysisofcovariance.,7,MCAcanbeextendedbeyondmultipleregression,forexample,itcanbeextendedtologisticregressionandCoxregression.,8,MCAspecifiesthelinearmodelasfollows:
9,MCAisastatisticaloptionwiththeANOVAprocedure,10,Anexample,Toexaminetheeffectsofplaceofresidence,ethnicityandeducationlevelonwomensageatfirstmarriage,ANOVAVARIABLES=afmBYuandr(1,2)ethnic(1,2)educat(1,5)/MAXORDERSNONE/STATISTICSMEANMCA/METHODEXPERIM.,11,12,13,14,TheMCAoutputshowstheestimated(orpredicted)meansofthedependentvariableforeachcategoryoftheexplanatoryvariables,unadjustedandadjustedfortheeffectsoftheotherexplanatoryvariablesinthemodel.Italsoshowstheunadjustedandadjusteddeviationsfromthegrandmean.Therefore,thepredictedmeanminusthedeviationforeachcategoryisalwaysthesameandisequaltothegrandmean.predictedmeandeviation=grandmeanThe“deviationsadjustedforfactors”areequivalenttotheb1,b2,bncoefficientsaftercontrollingfortheeffectoftheotherexplanatoryvariables.,15,Eachcombinationofthebcoefficientswillgivetheestimatedvalueofthedependentvariableforarespondentwiththecorrespondingcharacteristics.,16,Acomparisonoftheunadjustedandadjustedmeansforeachcategoryoftheindependentvariablesshowswhathappenswhenanadjustmentismadefortheeffectsoftheothervariables.Thelargertherangeinthedeviationsamongthecategoriesofeachexplanatoryvariable,thegreaterthesignificanceofthatfactorinaffectingthedependentvariable.,17,Ifwerunmultipleregression,18,19,Multipleclassificationanalysisisanextensionofmultipleregressionthatallowsustouseregressioncoefficientstopredictthemeanvaluecontrollingfortheeffectofotherpredictorsinthemodel.MCAissimplyawayofsolvingtheregressionequation.,20,Unadjustedmeans,Unadjustedmeanscanbeobtainedfromsimplelinearregression:
“unadjusted”means“withoutcontrols”:
21,Adjustedmeans,Adjustedmeansareobtainedfrommultiplelinearregression:
“adjusted”means“withcontrols”:
22,Adjustedmeans,Whenwecalculatemeanageatfirstmarriagebyresidence,ethnicityandeducationarethecontrolvariables;Whenwecalculatemeanageatfirstmarriagebyethnicity,residenceandeducationarethecontrolvariables;Whenwecalculatemeanageatfirstmarriagebyeducation,residenceandethnicityarethecontrolvariables.,23,Adjustedmeans,Ingeneral,whenweconsideradjustedmeansforonepredictorvariable,alltheothervariablesarethecontrolvariables.Statisticalcontrolsareintroducedbyholdingthecontrolvariablesconstantattheirmeanvalues.,24,Holdingthecontrolvariablesconstantattheirmeanvalues,Foracontinuousvariable,suchasage,themeanvalueseemsanappropriatemeasure.Inessencewearecontrollingfortheaverageexperienceorperson.However,theuseofameanforadichotomousdummyvariableseemsartificialaseachindividualcanhaveavalueof0or1butnoonecanhaveavalueinbetween0and1.However,ifwethinkofthemeanofadichotomousvariableasaproportionitsusemakesmoresense.Herewearecontrollingfortheproportionofmales(forsex)ortheproportionofpeoplewithcollegeeducationetc.,25,TosolvetheregressionequationusingExcel,ThefollowingexamplepresentsawayofsettingupanMCAcalculationtableinExcel.Weneedthecoefficientsoftheregressionmodel.ThesecanbecopiedstraightfromtheSPSSoutputintoExcel.ThenweneedtogeneratethemeanvalueofeachindependentvariableandcopythesevaluesintoExcel.Wegivetheconstantavalueof1inthemeancolumnsothatwhenwemultiplythecolumnsitremainsattheoriginalvalue.,26,27,IncludingintervalindependentvariablesinMCA,IntervalscalevariablescanbeincludedinMCAascovariates.Theirroleinthemodelcanbeviewedintwowaysconceptually:
asacontrolvariableasanotherexplanatoryvariable,28,SPSSSyntax,29,Anexample,Toexaminetheeffectsofplaceofresidence,ethnicityandeducationlevelonwomensageatfirstmarriage,whencontrollingforwomensage,ANOVAVARIABLES=afmBYuandr(1,2)ethnic(1,2)educat(1,5)WITHage/COVARIATESWITH/MAXORDERSNONE/STATISTICSMEANMCAREG/METHODEXPERIM.,30,31,32,33,34,35,36,Thethreeequationsarethesame:
37,MCAAdaptedtoLogisticRegression,WhenMCAisadaptedtologisticregression,bothunadjustedandadjustedvaluesoftheresponsevariablecanbecalculated,justasinordinaryMCA.,38,Theunadjustedvaluesarebasedonlogisticregressionthatincorporateonepredictorvariableatatime,andtheadjustedvaluesarebasedonthecompletemodelincludingallpredictorvariablessimultaneously.,39,UnfortunatelySPSSdoesnotincludeMCAprogramsforlogisticregression,wehavetoconstructtheMCAtablesfromtheunderlyinglogisticregressions.,40,AnIllustrativeExample,ToillustratehowMCAcanbeadaptedtologisticregression,weconsidertheabortionexample:
theabortionuseeffectofage,pregnancy,residence,ethnicity,andeducation.,41,Variables,P:
estimatedprobabilityofabortionuseAgeisclassifiedintotwobroadgroups:
15-34and35-49Numberofpregnanciesinthreecategories:
1,2,and3andoverResidence,ethnicity,andeducationcategorizedasformerly,42,43,Whencalculatingthevalueoffromthefittedregressionforeachcategoryofaparticularindependentvariable,dummyvaluesofthatvariablearesettobecombinationsofonesandzeroswhileallothervariablesarecontrolledbyholdingthemconstantattheirmeanvalues.,44,AdjustedP,Exponentiationofthevaluesofyieldstheadjustedvaluesof(),AdjustedvaluesofParecalculatedas:
45,Animportantpoint,UnlikeOLSregressioninwhichsubstitutionofmeanvaluesfortheindependentvariablesalwaysyieldsthemeanvalueofthedependentvariable,thisisgenerallynotthecaseforlogisticregression.,46,Inlinearregression,substitutionofmeanvaluesfortheindependentvariablesalwaysyieldsthemeanvalueofthedependentvariable,47,Thisiscalculatedfromtheregressionequation,48,Overallmeanageatfirstmarriagecalculatedfromthesample,Thisisdirectlycalculatedfromthesample,49,However,thevalueofoverallPproducedfromthelogisticregressionequationisgenerallynotidenticaltotheobservedvalueofoverallP.,50,51,Thisiscalculatedfromtheregressionequation,52,Thisisdirectlycalculatedfromthesample,53,54,InorderforthelogisticregressiontoproducetheadjustedvalueofoverallPthatisidenticaltotheobservedvalueofoverallP,theconstantterminthefittedregressionequationneedstobefirstadjusted.,55,ThisisdonebysubtractingthesumproductofthefittedcoefficientsandthemeanvaluesoftheindependentvariablesfromthenaturallogvalueoftheobservedoverallP.Thisyieldsanewconstanttermvaluewhichisthensubstitutedfortheoriginalone(a)inthefittedequation.,56,57,TheillustrativeexampleinExcel,Adjustedabortionprobabilitybyage,pregnancynumber,residence,ethnicity,andeducation,58,CalculatingMCAinExcel,59,CalculatingMCAinExcel,
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